Finding the minimum connected dominating set (MCDS) is a key problem in wireless sensor networks, which is crucial for efficient routing and broadcasting. However, the MCDS problem is NP-hard. In this paper, a new approximation algorithm with approximation ratio H( )+ 3 in time O n2 is proposed to approach the MCDS problem. The key idea is to divide the sensors in CDS into core sensors and supp...


 Let G be a connected graph. A set S of vertices in is 2-resolving hop dominating if and for every vertex x ∈ V (G)\S there exists y such that dG(x, y) = 2. The minimum cardinality called the domination number denoted by γ2Rh(G). This study aims to combine concept with sets graphs. main results generated this include characterization join, corona lexicographic product two graphs, as well ...

Let G be a connected graph. A set W ⊆ V (G) is resolving hop dominating of if in and for every vertex v ∈ \ there exists u such that dG(u, v) = 2. S 1-movable S, either {v} or ((V S) ∩ NG(v)) (S {v}) ∪ {u} G. The domination number G, denoted by γ 1 mRh(G) the smallest cardinality This paper presents characterization sets join, corona lexicographic product graphs. Furthermore, this determines ex...

We give the first linear kernels for Dominating Set and Connected Dominating Set problems on graphs excluding a fixed graph H as a topological minor. In other words, we give polynomial time algorithms that, for a given H-topological-minor free graph G and a positive integer k, output an H-topological-minor free graph G′ on O(k) vertices such that G has a (connected) dominating set of size k if ...

Abstract. In this paper, connected domination in fuzzy graphs using strong arcs is introduced. The strong connected domination number of different classes of fuzzy graphs is obtained. An upper bound for the strong connected domination number of fuzzy graphs is obtained. Strong connected domination in fuzzy trees is studied. It is established that the set of fuzzy cut nodes of a fuzzy tree is a ...

A mobile ad-hoc network (MANET), a set of wirelessly connected sensor nodes, is a dynamic system that executes hop-by-hop routing independently with no external help of any infrastructure. Proper selection of cluster heads can increase the life time of the Ad-hoc network by decreasing the energy consumption. Although different methods have been successfully proposed by researchers to tackle...

In an efficient design of routing protocols in ad hoc wireless networks, the connected dominating set (CDS) is widely used as a virtual backbone. To construct the CDS with its size as minimum, many heuristic, meta-heuristic, greedy, approximation and distributed algorithmic approaches have been proposed in the recent years. These approaches mostly concentrated on deriving independent set and th...

A vertex w in a connected graph G strongly resolves two distinct vertices u and v V (G) if is any shortest u-w path or v-w path. set W of strong resolving every are resolved by some W. S subset hop dominating for ∈ \ there exists such that dG(u, v) = 2. The smallest cardinality called the domination number G. This paper presents characterization sets join, corona lexicographic product graphs. F...

Let G be a graph. A set S ⊆ V (G) is hop dominating of if for every v ∈ (G)\S, there exists u such that dG(u, v) = 2. The minimum cardinality γh(G) the domination number G. Any γh-set which intersects transversal set. γbh(G) in In this paper, we initiate study domination. First, characterize graphs whose values are either n or − 1, and determine specific some graphs. Next, show positive integer...